[ $LaMeO_3$ ](Me = Cr, Co) powders were prepared using the polymeric precursor method. The effects of the chelating agent and the polymeric additive on the synthesis of the $LaMeO_3$ perovskite were studied. The samples were synthesized using ethylene glycol (EG) as the solvent, acetyl acetone (AcAc) as the chelating agent, and polyvinylpyrrolidone (PVP) as the polymer additive. The thermal decomposition behavior of the precursor powder was characterized using a thermal analysis (TG-DTA). The crystallization and particle sizes of the $LaMeO_3$ powders were investigated via powder X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), and particle size analyzer, respectively. The as-prepared precursor primarily has $LaMeO_3$ at the optimum condition, i.e. for a molar ratio of both metal-source (a : a) : EG (80a : 80a) : AcAc (8a) inclusive of 1 wt% PVP. When the as-prepared precursor was calcined at $700^{circ}C$, only a single phase was observed to correspond with the orthorhombic structure of $LaCrO_3$ and the rhombohedral structure of $LaCoO_3$. A solid-electrolyte impedance-metric sensor device composed of $Li_{1.5}Al_{0.5}Ti_{1.5}(PO_4)_3$ as a transducer and $LaMeO_3$ as a receptor has been systematically investigated for the detection of NOx in the range of 20 to 250 ppm at $400^{circ}C$. The sensor responses were able to divide the component between resistance and capacitance. The impedance-metric sensor for the NO showed higher sensitivity compared with $NO_2$. The responses of the impedance-metric sensor device showed dependence on each value of the NOx concentration.